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Simplifying 9y2 + 16y + -20 = 0 Reorder the terms: -20 + 16y + 9y2 = 0 Solving -20 + 16y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 1.777777778y + y2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 1.777777778y + 2.222222222 + y2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 1.777777778y + y2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 1.777777778y + y2 = 0 + 2.222222222 1.777777778y + y2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 1.777777778y + y2 = 2.222222222 The y term is 1.777777778y. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778y + 0.7901234570 + y2 = 2.222222222 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778y + y2 = 2.222222222 + 0.7901234570 Combine like terms: 2.222222222 + 0.7901234570 = 3.012345679 0.7901234570 + 1.777777778y + y2 = 3.012345679 Factor a perfect square on the left side: (y + 0.888888889)(y + 0.888888889) = 3.012345679 Calculate the square root of the right side: 1.735611039 Break this problem into two subproblems by setting (y + 0.888888889) equal to 1.735611039 and -1.735611039.Subproblem 1
y + 0.888888889 = 1.735611039 Simplifying y + 0.888888889 = 1.735611039 Reorder the terms: 0.888888889 + y = 1.735611039 Solving 0.888888889 + y = 1.735611039 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + y = 1.735611039 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + y = 1.735611039 + -0.888888889 y = 1.735611039 + -0.888888889 Combine like terms: 1.735611039 + -0.888888889 = 0.84672215 y = 0.84672215 Simplifying y = 0.84672215Subproblem 2
y + 0.888888889 = -1.735611039 Simplifying y + 0.888888889 = -1.735611039 Reorder the terms: 0.888888889 + y = -1.735611039 Solving 0.888888889 + y = -1.735611039 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + y = -1.735611039 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + y = -1.735611039 + -0.888888889 y = -1.735611039 + -0.888888889 Combine like terms: -1.735611039 + -0.888888889 = -2.624499928 y = -2.624499928 Simplifying y = -2.624499928Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.84672215, -2.624499928}
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